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ON A PERMUTABLITY PROBLEM FOR GROUPS
TAERI, BIJAN 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.20 No.1
Let m, n be positive integers. We denote by R(m,n) (respectively P(m,n)) the class of all groups G such that, for every n subsets $X_1,X_2\ldots,X_n$, of size m of G there exits a non-identity permutation $\sigma$ such that $X_1X_2{\cdots}X_n{\cap}X_{\sigma(1)}X_{/sigma(2)}{\cdots}X_{/sigma(n)}\neq\phi$ (respectively $X_1X_2{\cdots}X_n=X_{/sigma(1)}X_{\sigma(2)}{\cdots}X_{\sigma(n)}$). Let G be a non-abelian group. In this paper we prove that (i) $G{\in}P$(2,3) if and only if G isomorphic to $S_3$, where $S_n$ is the symmetric group on n letters. (ii) $G{\in}R$(2, 2) if and only if ${\mid}G{\mid}\geq8$. (iii) If G is finite, then $G{\in}R$(3, 2) if and only if ${\mid}G{\mid}\geq14$ or G is isomorphic to one of the following: SmallGroup(16, i), $i\in$ {3, 4, 6, 11, 12, 13}, SmallGroup(32, 49), SmallGroup(32, 50), where SmallGroup(m, n) is the nth group of order m in the GAP [13] library.
QUADRATIC RESIDUE CODES OVER ℤ<sub>9</sub>
Taeri, Bijan Korean Mathematical Society 2009 대한수학회지 Vol.46 No.1
A subset of n tuples of elements of ${\mathbb{Z}}_9$ is said to be a code over ${\mathbb{Z}}_9$ if it is a ${\mathbb{Z}}_9$-module. In this paper we consider an special family of cyclic codes over ${\mathbb{Z}}_9$, namely quadratic residue codes. We define these codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over finite fields.
GYM-Net: Graphical Y-branched Multi-tasking Network for Trajectory Prediction
Taeri Kim,Junseok Lee,Seongju Lee,Kyoobin Lee 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
For autonomous driving, the ability to predict the future from the past trajectory is crucial. In this study, a graphical Y-branched multi-tasking network (GYM-Net) is proposed. The GYM-Net predicts future trajectory from multi-scale graphical features using multi-task learning. The GYM-Net predicts both the final position after ten-time steps and the future trajectory after ten-time steps based on the previous trajectory of five-time steps. Using the NBA dataset that is widely used to predict the agents that are active in multi-agent trajectory predictions, we assessed the performance of our model. The performance of our model is 2.37 m, 2.31 m, 3.87 m, and 3.81 m for the evaluation metrics of avgADE, minADE, avgFDE, and minFDE, respectively. Compared with the performance of the graph U-Net, our model shows a decrease in error by 0.02, 0.04, 0.02, and 0.04, respectively. Consequently, our model can predict the trajectory of multiple dynamic agents.
Quadratic residue codes over Z_9
Bijan Taeri 대한수학회 2009 대한수학회지 Vol.46 No.1
A subset of n tuples of elements of Z_9 is said to be a code over Z_9 if it is a Z_9-module. In this paper we consider an special family of cyclic codes over Z_9, namely quadratic residue codes. We define these codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over finite fields. A subset of n tuples of elements of Z_9 is said to be a code over Z_9 if it is a Z_9-module. In this paper we consider an special family of cyclic codes over Z_9, namely quadratic residue codes. We define these codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over finite fields.
김태리(Taeri Kim),홍지원(Jiwon Hong),박노성(Noseong Park),김상욱(Sang-Wook Kim) 한국정보과학회 2020 정보과학회 컴퓨팅의 실제 논문지 Vol.26 No.3
피싱을 통한 사이버 범죄가 늘어나고 있다. 피싱이 초래하는 피해를 방지하기 위해 콘텐츠 기반, URL 문자열 기반 등 많은 피싱 URL 관련 연구들이 진행되어 왔다. 콘텐츠 기반 방법은 웹 페이지 콘텐츠를 다운로드하고 분석하는 방법으로, 보안상 위험이 따르는 단점이 존재한다. URL 문자열 기반 방법은 URL 문자열 패턴을 분석하고 이를 피싱 URL 탐지에 사용한다. 본 논문에서는 기존 연구로부터 확인된 피싱 URL의 경향에서 착안하여, URL 문자열을 그래프로 구축하고 Random Walk with Restart, Belief Propagation과 같은 그래프 추론 알고리즘과 DeepWalk, Node2vec과 같은 그래프 임베딩 기법을 통해 URL의 피싱 여부를 예측한다. 우리의 그래프 기반 피싱 URL 탐지 방법과 분류 알고리즘을 활용한 기존 피싱 URL 탐지 방법을 비교한 결과, 그래프 기반 방법이 모든 정확도 척도에서 더 높은 성능을 보였다. Cyber crime through phishing is on the rise. To prevent the damage caused by phishing attacks, many studies to detect phishing URLs such as content-based and string-based have been conducted. A content-based method is a method of downloading and analyzing web page content, which poses a security risk. The string-based method analyzes URL string patterns and uses them for phishing URL detection. In this paper, we construct a graph with URL strings based on the phishing URL trends identified from previous studies. And, we detect phishing URLs through the graph-based inference algorithms such as Random Walk with Restart, Belief Propagation, and graph embedding methods such as DeepWalk, Node2vec. As a result of comparing our graph-based phishing URL detection method with the conventional phishing URL detection methods, our method shows better prediction performance in all accuracy measures.
FULL NON-RIGID GROUP OF 2,3,5,6-TETRAMETHYLEPYRAZINE AS WREATH PRODUCT AND ITS SYMMETRY
Arezoomand, Majid,Taeri, Bijan The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.3
The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to deduce the character table of the full non-rigid molecule group (f-NRG) of 2,3,5,6-Tetramethylpyrazine The f-NRG of this molecule is seen to be isomorphic to the group $\mathbb{Z}_3{\wr}(\mathbb{Z}_2{\times}\mathbb{Z}_2)$, where $\mathbb{Z}_n$ is the cyclic group of order n, of order 324 which has 45 conjugacy classes. We determine the some properties and relations between characters of the group. Also, we examine the symmetry group of this molecule and show that its symmetry group is $\mathbb{Z}_2{\times}\mathbb{Z}_2$.